NBS TECHNICAL NOTE 864

'H-AU Of *

U.S. DEPARTMENT OF COMMERCE/ National Bureau of Standards

Cost Recovery in Pr

and Capacity Decisions for

Automated Information Systems
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, ( 3 ) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology,

the Institute for Computer Sciences and Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United

States of a complete and consistent system of physical measurement; coordinates that system

with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry, and commerce. The Institute consists of a Center for Radiation Research, an Office of Measurement Services and the following divisions: Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics — Nuclear

Sciences 2 — Applied Radiation 2 — Quantum Electronics s — Electromagnetics 3 — Time

and Frequency 3 — Laboratory Astrophysics 3 — Cryogenics 3

. THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to improved methods of measurement, standards, and data on the properties of well-characterized materials needed by industry, commerce, educational institutions, and Government; provides

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Radiation — Physical Chemistry.

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Environment * — Technical Evaluation and Application * — Fire Technology.

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research and provides technical services designed to aid Government agencies in improving cost effectiveness in the conduct of their programs through the selection, acquisition, and effective

utilization of automatic data processing equipment; and serves as the principal focus within

the executive branch for the development of Federal standards for automatic data processing

equipment, techniques, and computer languages. The Institute consists of the following

divisions: Computer Services — Systems and Software — Computer Systems Eng.neermg — Information Technology.

THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and

accessibility of scientific information generated within NBS and other agencies of the Federal Government; promotes the development of the National Standard Reference Data System and

a system of information analysis centers dealing with the broader aspects of the National Measurement System; provides appropriate services to ensure that the NBS staff has optimum

accessibility to the scientific information of the world. The Office consists of the following

organizational units:

Office of Standard Reference Data — Office of Information Activities - Office of Technical

Publications — Library — Office of International Relations.

t Headquarters and Laboratories at Gaithersburg. Maryland, unless otherwise noted; mailing .ddrws

Washington, D.C. 20234.

a Part of the Center for Radiation Research.

3 Located at Boulder, Colorado 80302.

* Part of the Center for Building Technology.
****** Library

MAY2oi$$ost Recovery in Pricing and Capacity

t^oT

6

' Decisions for Automated Information Systems

,U515t -

'"*

Ja-nesA.DeiRossi

Information Technology Division

Institute for Computer Sciences and Technology

National Bureau of Standards

Washington, D.C. 20234

Sponsored by

The National Science Foundation

Washington, D.C. 20550

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U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Issued April 1 975
V

-

Library of Congress Catalog Card Number: 75-600015

National Bureau of Standards Technical Note 864

Nat. Bur. Stand. (U.S.), Tech. Note 864, 60 pages (April 1975) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1975

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. 03.46:864).

Price $1.20
CONTENTS

Page

I. Introduction and Overview

2

II. Measuring Social Benefit

8

A. Direct Social Benefit ...... o B. Indirect Social Benefit . . . . [ [ ^

III. Maximizing Net Benefit -|2

IV. Demand and Capacity . ....... 13

A. The Demand Function

'* 15

B. Performance and Capacity

"

-| 7

V. On-Site Entry, Fixed Capacity ... 21

A. System Cost [ 21

1. Capacity Cost ! 23

2. Input Cost ....'! 24

3. Search Cost .25

4. Total Cost 25

B. Pricing Alternatives 27

VI. Remote Entry, Fixed Capacity 30

A. System Cost 30

1

.

Producer Cost 31

2. User Cost 32

3. Total Cost 33

B. Pricing Alternatives 35

C. Cost Recovery . 38

VII. Capacity Investment and Pricing 39

A. System Cost and Capacity 39

B. On-Site Entry 42

C. Remote Entry 44

VIII. Policy Implications 49

A. Public Goods 49

B. Semi -Public Goods 50

C. Automated Information Systems 51

Appendix A • 52

References 54

in

COST RECOVERY IN PRICING AND CAPACITY DECISIONS

FOR AUTOMATED INFORMATION SYSTEMS

by

JAMES A. DEI ROSSI*

ABSTRACT

This paper examines the cost-benefit implications of alternative pricing and capacity investment decisions for automated scientific and technical

information retrieval systems. Two typical systems are examined and numerical examples presented. In the first system, search requests are entered

on-site. The numerical examples show how setting price to maximize net

social benefit precludes total cost recovery and implies subsidization.

In the second hypothetical system, search requests are entered from remote

access terminals. Allowance is made for random arrival rates, and distinction is made between system charges to users and other user incurred

costs. With these refinements, the numerical examples show how, for certain

ranges of output, total cost recovery is consistent with the maximization of

net social benefit. The paper then examines the "public good" attributes of

scientific and technical information retrieval systems and concludes that

such systems can be viewed as "semi-public goods," since the information

stored has the characteristics of a public good while access to this information has the characteristic of a private good. Based on the public good

considerations and the numerical examples, the paper concludes that subsidization for the fixed costs is warranted to the extent that all reasonable

alternatives which maximize net social benefit preclude total cost recovery.

Key Words ; Automated information retrieval; cost-benefit; public good;

scientific and technical information; semi-public good; subsidization;

total cost recovery; user charges.

* Interplan Corp. , 100 N. Hope Avenue, Santa Barbara, CA 93110

1
COST RECOVERY IN PRICING AND CAPACITY DECISIONS

FOR AUTOMATED INFORMATION SYSTEMS

I. INTRODUCTION AND OVERVIEW

Should fees be charged for the use of scientific and technical information

products and services? And, if so, should such fees be set at a level that

will result in total cost recovery? Since the alternative to total cost

recovery is subsidization, the issue of total cost recovery is critical to

the future growth and development of automated scientific and technical

information retrieval systems that are fully or partially financed with

public funds. However, the answers to the questions posed have been clouded

by both the importance of scientific and technical information to the public

as a whole, and by the dominant role of publicly sponsored activities in the

areas of science and technology. Both of these factors have reinforced the

"public good" appearance of scientific and technical information in a nation

where the importance of free access to information has been a long-standing

tradition.

When scientific and technical information is viewed as a public good,

little attention is given to the role of price. Free library service and

the 1 0<t government publication are examples of the public good approach

wmcn has also been applied to the use of scientific and technical information

However, as the cost of providing access to scientific and technical
information has increased, attitudes have shifted to considering the treatment

of such information as a private good, and numerous opinions have been expressed

that price should be used to insure total cost recovery.

In contrast to these opposite poles of thought, the conclusion of this

paper is that scientific and technical information products and services are

in the domain of what has been referred to as the "semi -public" good. Unlike

public goods, it is felt that the provision of scientific and technical

information products and services should utilize price and the market place

as a means for determining the allocation of resources. However, unlike the

provision of private goods, total cost recovery is not viewed as the

appropriate criterion for establishing prices.

Public goods, which are "enjoyed but not consumed," are largely unaffected

by the number of persons benefiting from them. National defense and law and

order are familiar examples of such public goods. Private goods, however, are

consumed, in the sense that each person's enjoyment affects the availability

of these goods to others, and the cost of producing these goods is roughly

proportional to the number of persons benefiting. The ideas and concepts

constituting the body of scientific and technical knowledge have the property

of a public good, since they are not consumed when enjoyed. However, access

to these ideas and concepts, as provided for through information services and

products has the attribute of a private good in that the numbers of persons

utilizing them affects both cost and availability.
Because of the semi -public-good nature of scientific and technical

information products and services, it can be concluded that net social

benefit rather than total cost recovery should be taken as the criterion

for establishing appropriate prices.* Accepting this conclusion, several

questions immediately follow: How can net social benefit be measured? What

are the pricing rules for maximizing net social benefit? Does pricing

according to such rules preclude total cost recovery and imply subsidization

for automated scientific and technical information retrieval systems?

The body of this paper begins by examining the role of market prices

in measuring social value, using the conventional economic concept of

"consumer surplus." Based on this concept, market responses as reflected

in the demand for an information product or service can be used to derive

a measure of the total social value of that product or service. The

difference between this total social value and the cost of producing that

same product or service is taken as the net social benefit derived from its

production and consumption.

Using standard mathematical techniques, Appendix A shows that the

maximization of net social benefit occurs when price is set equal to marginal

cost.** In contrast, total cost recovery implies setting price equal to average

cost. Thus, the effect of using the maximization of net social benefit to

establish price for the services and products of automated scientific and

*The focus of this paper is on publicly operated or publicly funded access to

scientific and technical information. However, the logic can be equally applied

to such access provided by information centers within private organizations. In this latter case, it would be argued that the information service department

should set its prices using the benefit of the organization as a whole to establis

prices, rather than cost recovery for that department.

**Marginal cost is the amount by which total cost increases for each additional

unit of output and, thus, can be thought of as the cost of producing the last

unit of output.
technical information retrieval systems rests on the relationship between

marginal cost and average cost in the operation of such systems. If marginal

cost is greater than or equal to average cost, setting price equal to marginal

cost would be consistent with the goal of total cost recovery. However, if

marginal cost is less than average cost, total cost will not be recovered,

and some form of subsidization is implied. The question then becomes: Is

the value of total benefit greater than the total cost of production plus

the implied subsidy; i.e., is there a positive net benefit? Unless the answer

to this question is affirmative, there is no economic justification for

subsidization.

The precise relationship between marginal cost and average cost will

vary among systems, based on the unique organizational and technological

characteristics of each. However, typical relationships between these two

types of cost for automated scientific and technical information retrieval

systems can be established by a careful analysis of operational characteristics

and cost factors based on actual experience. Such relationships are developed

in this paper for two specific, hypothetical systems to illustrate how the

techniques of operations research and economic analysis can be used to evaluate

prices for actual systems, and to provide numerical examples of the application

of cost-benefit analysis to both pricing and capacity investment decisions.

In the first hypothetical system, requests for searches are entered

on-site. In the second, requests for searches are entered from remote access

terminals. Thus, the two systems chosen are representative of two major classes

of automated information retrieval systems. Interestingly, the cost relationships

for each type of system differ dramatically. For the on-site entry system,

average cost is always greater than marginal cost, implying the need for some

form of subsidy if a socially optimum level of output is to be sustained. For
the remote entry system, distinction between system charges to the users

and other user incurred cost, and allowance for the congestion implications

of the random nature of remote-entry arrival rates, show that marginal

cost can be greater than average cost for certain ranges of output.

The ranges of output over which marginal cost is greater than average

cost depend on the rate of search requests relative to the total output

capacity of a system. Therefore, before presenting the cost data and examples,

the paper examines the concept of capacity and the relationships among

capacity, rate of search request arrivals, and search time. Using search

time required per search as a measure of performance, it is shown how the

specification of minimum performance (search time) criteria can be used to

identify the "effective capacity" of an automated information retrieval

system; i.e., the maximum search request rate that can be processed without

violating the specified performance requirements. It is at this point that

the concept of congestion and its impact on search time are introduced. In

the later sections, effects of increased search time on marginal cost are

examined.

Using the cost data, the performance criteria, and various postulated

levels of demand, numerical examples are developed to examine the cost-benefit

implications of alternative pricing and capacity investment decisions. The

general implications of the specific findings are then discussed. In all,

there are four examples presented, two for each system. In the first two

examples, the impacts of pricing policy on net social benefit and total

cost recovery are examined, for a given and fixed output capacity. In the

other two examples, the net social benefit and total cost recovery implications
of pricing alternatives together with char ;s in capacity are examined. A

summary tabulation of these examples, indicating the order in which they are

presented is as follows:

On Site Remote Access

Fixed Capacity Case 1 Case 2

Variable Capacity Case 3 Case 4

The results for the on-site entry examples show how maximizing net

social benefit will generally be inconsistent with total cost recovery for

this type of system. Setting price equal to marginal cost will result in

increased output, lower user cost, and increased net social benefit than

would occur by setting price equal to average cost in order to recover total

cost. However, because marginal cost is likely to be constant for this type

of system, setting price equal to marginal cost also will entail a loss to

the extent of the total fixed cost of the system. Thus, a socially optimum

price with on-site entry implies the recovery only of costs which vary with

the level of output and the subsidization of fixed costs. This roughly is

equivalent to subsiziding the "public good" component of the system and

recovering the costs of the "private-good" component.

The results for the remote-entry examples show that total cost recovery

and the maximization of net social benefit are not always inconsistent. To

demonstrate this it is necessary to distinguish between system charges to

the users and other user incurred costs; i.e., to recognize that not all

user costs are paid to the producer. With this distinction and appropriate

allowance for the increases in search time that occur as utilization rates

increase, it is shown how, under certain circumstances, it is possible to set

price so as to maximize net social benefit and still recover total cost.
The major implication of these findings is, therefore, that the

decision to subsidize rather than to set price so as to recover full cost

should be based on careful analysis and not simply on the public-good-concept.

Only if it can be demonstrated that total cost recovery is not feasible for

all reasonable pricing and capacity investment alternatives, should subsidization

occur. And, second, if subsidization is given, it should not exceed the value

of the fixed cost or public-good component of the product or service.

II. MEASURING SOCIAL BENEFIT

From the viewpoint of promoting an economically efficient use of resources,

price must be understood as a mechanism for allocating scarce resources. The

distinction between price as an allocating mechanism and price as a device for

recovering cost is an important one. Market prices, when understood as

mechanisms for allocating scarce resources, can also be used to develop measures

of social benefit. A brief review of the role of markets and prices in a

market economy can be used to illustrate these ideas.

A. Direct Social Benefit

In deciding on specific purchases, individuals are continually weighing

alternatives and determining how to spend or save their limited resources.

Similarly, private firms select among alternatives in making their investment

decisions. When markets are functioning properly, prices are bid up to th

point where the available supply is allocated to the consumers who are

willing to pay the highest price. Similarly, producers who are willing to

pay the highest price for a resource are those whose product is most highly

valued by members of society; i.e., the prices the producer is willing to

pay for input resources are largely determined by the prices consumers are
willing to pay for the product or output of that producer. In this way, the

prices consumers and producers pay reflect the values and priorities of

society.

Thus, under appropriate conditions, the market approach provides a

means for both efficient output distribution and efficient productive resource

allocation:

"... the conditions for pricing to work are fairly

simple: users must be unable to obtain any scarce resource at a zero price; social and private direct

benefits must be identical, so that neither benefits

nor costs are incurred except by the buyer and seller;

and prices must be free to vary without regard to the

cost of production. (These are rigorous requirements;

in fact, pricing will usually work if these requirements

are loosely satisfied.)" [13]

When these conditions are met, the value of a good or service to consumers

or buyers can be considered the value of that product to society. Therefore,

the total benefit (value) to society derived from the consumption of a good

or service when the conditions outlined above are met is the sum of the

benefits (values) to each purchaser.

The demand curve, which shows the number of units purchasers are willing

to purchase at a given price provides a means for calculating this sum of

individual benefits. Figure 1 shows such a demand curve, labeled DD'. By

the reasoning outlined above, the total social benefit (TB) derived from

the consumption of Q units is given by the area under the demand curve

from zero to Q; i.e., the area DBQO.

For a given price, P, a quantity, Q, will be demanded. The total revenue

(TR) from providing Q units at price, P, is given by the area under tht
Q.

S-3

oo

s-0)E

incoo

QiC>

rt3 o

0)

s0>u

10
rectangle PBQO. The remaining area, DBP is "consumer surplus." Consumer

surplus (CS) is the difference between the price that consumers pay for a

good or service and the amount they would be willing to pay rather than do

without. Thus, TB = TR + CS. By definition, the corresponding net social

benefit (NB) is the total social benefit less the total cost (TC) of producing,

the Q units; i.e., NB = TB - TC*

B. Indirect Social Benefit

Although direct social benefit as defined above is the measure that will

be used in the following examples, it is well to recognize that, in the actual

evaluation of systems, indirect benefits and externalities should also be

considered. The recent report of the Panel of Economics of the Science

Information Council [5, p. 40-51] presents a useful discussion on the issue

of quantifying total indirect and direct benefit.

The direct benefit calculation based on market response and consumer

surplus can be viewed as an approximate lower bound on net benefit, as the

Report of the Task Group on the Economics of Primary Publications points

out [9, p. 8]. Following this logic as presented for journals, the relationship between the direct and total social value of automated scientific and

technical information system services can be expressed as:

Total Social _ Value to current

+ Value to others, including

value " users future generations

*In cases where cost or benefits are external to the market and not reflected

in the cost of production or the market price, social cost (benefit) is not

equal to private cost (benefit). In these cases there is said to be a market

failure due to externalities. With external benefits, total benefit will be

understated. With external costs total benefits will be overstated. The

allocation by market price is still viewed, in principle, as efficient when

external cost is involved if the net benefit is high enough to compensate

for the external costs.

11
And, the first term also consists of two parts: Current users receive

information both directly via their own use of the systems, and indirectly,

via contacts with others who have used them. Thus,

Value to current _ Current direct

+ Current indirect

users value value

The measure of net benefit described reflects only the first term of this

second equation, current direct benefit.

III. MAXIMIZING NET BENEFIT

Using the measure of direct social benefit described above, methodology

for evaluating alternative pricing and capacity investment decisions, in

terms of their impact on net benefit, can be applied. The derivation of the

net-benefit-maximizing price is described in Appendix A for both the general

case and the case where there is a constraint on output capacity. The appendix

shows that for the general case, net social benefit is maximized when

P = MC, (1)

where

P = price

and

MC = marginal cost,

the cost of producing the last unit of output. In contrast, when the objective

is to maximize producer benefit (profit) rather than net social benefit, the

maximizing condition is MC = MR, where MR (marginal revenue) is the increase

in total revenue from the sale of the last unit of output.

When the demand curve has a negative slope, some degree of monopoly or

market power exists. This occurs when the size of the market is small relative

to the producer and there is some distinctness or uniqueness in his product.

12
With a negative slope on the demand curve, the profit maximizing objective will

lead to higher prices and lower levels of output. This is shown in Figure 2

where MR intersects MC at Ql < Q and the price required to hold demand at that

level is PI > P.

If an output capacity constraint is operative, as would occur when the

demand curve intersected the vertical section of the MC curve at capacity

output, Q*, as shown in Figure 2 by the point A, the net benefit maximizing

price would be:

P = MC + X, (2)

where X is the vertical distance from the horizontal section of the MC

curve to the point of intersection. It is the amount over the value of MC

on the horizontal section which must be added to price in order to restrict

demand to a level consistent with capacity.

IV. DEMAND AND CAPACITY

In this and the following sections hypothetical data are introduced

to illustrate the application of cost-benefit analysis to pricing and

capacity investment decisions, using the maximization of net social benefit

as the criterion of evaluation. First, the demand function used in the

examples presented is described. Second, a simple queuing model is

presented as a basis for defining capacity. Next, system costs are

defined and several pricing and capacity investment alternatives are

examined and evaluated in terms of their impacts on net social benefit

and cost recovery.

13
co c&Iwo

"oE

*-o. O

CM*3

0>

Q.

14
A. The Demand Function

There are of course many factors which affect the demand for any good

or service, including information services. The major ones which would

be part of a comprehensive demand analysis include:

1. The price and quality of the good or service.

2. The prices and quality of competing and complementary goods and services.

3. The number of buyers.

4. Buyer preference and income.

For relatively short time periods, buyer characteristics, including

number, preferences, and income, can be taken as given and assumed to

remain essentially unchanged. Similarly, the assumption that the prices and

characteristics of competing and complementary goods and services remain

unchanged is a reasonably accurate assumption for competitive markets for

short time periods.

Quality of service has many dimensions. Characteristics such as relevancy,

recall and precision are important [3, 18]. To keep the illustration manageable,

only coverage will be explicitly treated in the demand analysis, and it will be

treated through a surrogate variable: data base size. With these ground rules,

demand, Q, can be expressed as a general function of price, P (cost to the user),

and data base size, N;

Q = f(P.N) (3)

The existence of a relationship between price and demand is, of course,

well documented. Evidence of the impact of "data base" size can be found

in [2, p. 27, 29; 6, p. 645].

15
For purposes of examining the benefit implications of alternative

price and capacity decisions, the "price elasticity of demand" is an

important demand function characteristic. Price elasticity, a, shows,

the proportional change in Q for a proportional change in P: -m w

If the absolute value of a is greater than one, demand is said to be elastic,

If it is less than one, demand is said to be inelastic. Inelastic demand

curves have steeper slopes than elastic demand curves, and the implications

of this difference are many. As an example, the difference between marginal

revenue and average revenue is greater the less elastic demand is. Thus,

average cost pricing will lead to a higher price and lower level of output

relative to marginal cost pricing the more inelastic the demand curves

are (see Figure 2).

Because of its reasonableness from a conceptual point of view and its

elasticity properties, the following functional form for the demand function

will be used in the examples which follow:

q = AeaP

e

BN

(5)

This form has the property that elasticity is proportional to the values

of the variables. Thus price elasticity for this form is given by a = -aP.

Similar calculations can be made for N. However, since the primary

interest is in the effect of price changes on demand, changes in N will be

viewed as quality related changes which shift the curve relating P and Q.

The value of 3 for equation 5 will be chosen so as to make the value of

3N = .4 [6, p. 645] for an assumed data base size of 350,000 documents.

16
To calculate total benefit for different values of Q, the integral of

the inverse of this demand function is used:

TB = V P(Q)dQ (6)

For the first illustration, the demand curve will be chosen so as to

intercept the average cost curve at Q=20,00Q. Such a curve with a chosen

so as to make aP = -1.25 at 20,000 is shown in Figure 6. Choosing the point

of intersection and specifying the elasticities determines the value of A

as well as the values of a and 8, so that all the values needed to calculate

total benefit for any specified quantity, q, are known.

B. Performance and Capacity

Although a uniform level of demand will be assumed over each 8 hour day,

arrivals of requests will still be somewhat random, introducing an element of

irregularity. Similarly, the amount of time required to service each request

will fluctuate from search to search. With these elements of randomness, the

performance of an automated information retrieval system is subject to random

flaws and congestion, even under the assumption of uniform loading. When

congestion occurs, queues develop, waiting time increases and performance

degrades.

The concept of intensity of utilization or rate of utilization affords

the simplest measure of congestion. It is defined as:

P

= X _mean requests per unit of time , < p < 1 (7) u mean service per unit of time

Thus, X is the mean arrival rate; y is the mean service rate, and 1/u is

the mean service time, S.

17
To illustrate the impacts of congestion on performance, a simple queuing

model is used. The automated information system in the example will be

viewed as a "single-server, no-loss" system, in which arrival rates are

described by a Poisson distribution and service times follow a negative

exponential distribution (see 11 and 21 for a discussion of these concepts).

With these assumptions, the mean waiting time, W, is [26, p. 318-319]:

W = __pS_ (8)

(1-p)

From this expression, it can be seen how waiting time increases as the

intensity of utilization, p, increases and approaches one.

Service time for an automated information retrieval system has

three components.

1. Input time : This is the time required to input the keywords of the

search into the computer.

2. Search time : This time depends on the complexity of the request, the

efficiency of the indexing system and the power of the system.

3. Output time : The time required to print out the search results.

Search times can be quite low. Assuming each request has 50 terms, with

a data base and system similar to those described in [22], the average

search time becomes (0.0003334 * 350 = ) 0.1166 minutes. With front-end

processers and off-line printing, the total service time could also be quite

low. For our example a total input/output time of 2 minutes will be

assumed initially, which means that S = 2.1166 minutes and y = .4725.

18
Assuming an 8 hour day, a 5 Hav week and 52 weeks per year gives

124,800 minutes per year of operation. The mean arrival rate per minute,

X, can be expressed as 124,800 minutes per year divided into the number of

requests per year. Thus, given S, the values of p and W can be calculated

as a function of the annual number of requests by inserting S, 1/S, and X

into equations 7 and 8.

The expected waiting time is one major element of a minimum-requiredperformance criterion for an automated information retrieval system. However,

since W is a random variable, random fluctuations will occur for any given

level of utilization. A fully operational performance criterion also requires

the specification of a level of confidence that the maximum waiting time

will not exceed a given value. These levels of confidence are referred to as

"percentiles." The (l-a)-percentile is the probability that, on the average,

(1-a) x 100 percent of the requests will have a waiting time less than t,

and can be expressed as [26, p. 318-319]:

W(t) = (1-a) = l-pe' (y_A)t

(9)

For the examples, the maximum waiting time required is set at 10 minutes

to prevent excessive waste of input resources. The expected waiting time,

W, and W(10) for a = .01, .05, .10 are shown in Figure 3 on semi -logarithmic

coordinates for various annual numbers of requests, Q, and corresponding

intensities of utilization, p. These calculations show that W=10 when

Q=48,700 and p=.83.

However, when at Q=48,700, W(10)=.64. This means that on the average

about 36 percent of the requests will have a waiting time greater than

10 minutes (i.e., a = .36). To achieve a higher probability that W will not

exceed 10 minutes requires that fewer searches be processed. For example

19
100.0

w

10.0

vt

0>E

iWll0)=.90

W(I0) = .95

1.0

0.1

Wll0) = .99

Figure 3 waiting Time and Percentiles

20
to maintain W(10) > .90 would require that the number of requests, Q,

be less than or equal to 36,000. Similarly, W(10) >. .95 requires

Q S 30,000 and W(10) >_ .99 requires Q 07,000.

For the examples, the value of W(10) will be set at .95. By so doing

the "effective capacity" of the system with S = 2.1166 is set at 30,000 search

requests per year. This means that pricing alternatives for the capacity size

will be required to maintain price sufficiently high to insure that the

number of searches demanded will be 30,000 or less.

V. ON-SITE ENTRY, FIXED CAPACITY

To illustrate the application of cost-benefit methodology in the

economic evaluation of alternative pricing decisions, hypothetical, but

realistic, cost data will be combined with the capacity criteria and

demand function previously described. In this section, a system with

on-site entry, together with its costs will be presented. Then, the

impact of alternative short-run (fixed capacity) pricing decisions on

net social benefit will be examined. Following this, a remote entry

system will be described and similar pricing alternatives examined.

Finally, the costs of increasing capacity will be discussed, capacity-cost

relationships postulated, and alternative pricing and capacity investment

decisions for both systems examined.

A. System Cost

The literature on the costs of information retrieval systems is

fairly extensive. Annual surveys can be found in a separate chapter of

21
each Annual Review of Information Science and Technology [4]. A particularly useful study of cost is contained in a recent book by Bryant and

King [3, p. 36-87], which contains a model of the cost of retrospective

information systems based on work performed for the American Psychological

Association [14]. A modified version of this model will be used as the

basis for the analysis of scientific information retrieval system cost.

Bryant and King point out that "the total cost of any given retrospective search system is composed of three types of costs:

1. Fixed costs (capacity) . . .

2. Variable costs dependent on the number of items input into the

system, and

3. Variable costs dependent on the number of searches conducted."

[3, p. 73]

Symbolically, this can be expressed as:

TC = F + bQ (10)

or TC = f + aN + bQ, (11)

where TC = Total Cost per year

F = Annualized total fixed cost

f = Annualized fixed cost associated with capacity

a = Cost per item input

b = Cost per search

N = Number of items input per year

Q = Number of searches per year

Other assumptions of the Bryant-King model are: "on-line (on-site)

system (inputting), including manual indexing for input, a thesarus to use

for input as well as searching, user requests processed through an intermediary by telephone or in writing, and searches that, on the average,

retrieve 80 per cent of the relevant items. Screening is performed on

search output, and abstracts of the identified documents are sent to the

user." [3, p. 73-74]

22
With the cost model for the system as described, Bryant and King

examine the questions of pricing for various cost allocation rules, assuming

that four products and services are sold:

1. Restrospective Searches

2. Tape Sales

3. Current Awareness Services

4. Recurring Bibliographies

The major characteristics of the cost curves do not change under the various

cost allocation assumptions used in the book. For the sake of ease of

exposition, it will be assumed in the example that only retrospective

searches are provided so that there are no additional costs and no allocation

considerations to be examined.

1. Capacity Cost

For analyzing fixed cost, Bryant and King identify "subsystems" with

fixed costs:

1. User/ system interface

2. Input

3. Search

4. Screening

5. Presentations

The fixed cost associated with each subsystem includes staff, space

rental and equipment costs. The total fixed capacity cost then is:

f = Ci + C 2 + C 3 + C* + C 5 , (12)

23
where each of the C. are the fixed costs associated with each of the

correspondingly numbered subsystems. For example, the following values

are assumed:

Ci = fixed cost of user/system interface are

$2,500, amortized over 5 years with a 6

percent capital recovery factor [l0> p. 113] = $ 595

C2 = fixed cost of input are $25,000, amortized

over 5 years with a 6 percent capital

recovery factor =

$ 5,925

C 3 = fixed search costs include: computer

rental, space, staff and fixed computer

storage space = $135,000

U = annual fixed cost of screening = $ 35,000

C5 = fixed cost of mailing set-up are $1,000,

amortized over 5 years with a 6 percent

capital recovery factor = $ 235

f = total annual fixed capacity cost = $176,755

2. Input Cost

To estimate annual input cost, a constant data base size of 350,000

citations will be assumed. The time over which the references cited in

this data base continue to have informational value is assumed to be 5

years, at which time they are removed from the data base file. Both of

these assumptions are somewhat simplifying but reasonable based on current

practice.

With these assumptions, 70,000 documents are added to the data base

each year, each requiring indexing, abstracting and keyboarding into

24
computer readable form. Computer-related processing costs for file

loading and removing of citations are relatively minor and assumed to be

provided as part of C3. The assumed annualized unit cost of inputting is:

C 6 = input cost per item for indexing, abstracting

and keyboarding are $0,575, amortized over

5 years with a 6 percent capital recovery factor = $0,136

Since C 6 = a in equation 11, total annual input cost (aN) is 0.136 x 350,000

$47,600.

3. Search Cost

It is assumed that an average of 125 documents are retrieved per

search and 25 documents are relevant and mailed. The unit search costs

are:

C7 = cost of user/ system interface per search = $ 15

C 8 = cost of screening per item retrieved per

search = $0,125

C9 = cost of mailing per relevant item per

search = $ .10

Thus, variable cost per search is:

b = C 7 + 125 x c 8 +25 x c 9 (13)

= $33.13

4. Total Cost

Total cost for various numbers of searches based on the cost factors

described are shown in Figure 4. The corresponding average total and

marginal (average variable) cost curves are shown in Figure 5. Total cost

25
10 20 30

Searches (Thousands)

Figure 4. Total Cost

20 30

Searches (Thousands)

Figure 5. Average and Marginal Cost

26
is a linear function of the number of searches, since marginal cost is

constant at $33.13. Average total cost declines over the whole range of

output and asymptotically approaches marginal cost, reflecting the

allocation of the fixed portion of cost to larger quantities of output.

These curves illustrate how a conflict between the goals of total

cost recovery and maximization of net social benefit can arise. When MC

is equal to some constant, b, up to capacity, and F > 0, as shown

in Figure 5, AC = (F/Q + b) so that MC < AC for all Q. When this occurs

the net benefit maximizing solution of P = MC is not consistent with total

cost recovery since TR = MC x Q < TC = AC x Q. This situation exists for

many automated information retrieval systems and is a factor in support

of subsidization of publicly financed systems. This issue will be discussed

further after a more detailed analysis of the outcomes of various pricing

and capacity Investment decisions.

B. Pricing Alternatives

For the on-site, fixed capacity example, the demand curve has been

chosen to intersect the average cost curve at Q=20,000 and AC=$45.35, as

shown in Figure 6. Thus, if price is set equal to average cost

(P=AC=$45.35), demand will be 20,000 and total revenue (P x Q) will just

equal total cost (AC x Q). At this point, total benefit is the area under

the demanc , „ calculated by integrating from Q equals to 20,000 using

equation 6; total cost is the area under the rectangle from the average

cost curve at 20,000 to each of the axes; and consumer surplus is the

difference between total benefit and total cost. These numbers are shown

below under the column headed P = AC.

27
2 70

oo

10

Total Revenue* Total Cost

m i&if&i&iM&Si/iriMfiMiM _L

5,000 10,000 15,000 20,000

Searches

J_

25,000 30,000

Figure 6 Average Cost, Morglnal Cost and Demand

On-Site Entry, Fixed Capacity

28
Impact of Changing To Marginal

Cost Pricing From Average Cost

Pricing with Capacity Constraint

(Dollars in Thousands)

Value at

P=AC

(Q=20,000)

Value at

P=MC

(Q=28,000)

Change

From P=AC

To P=MC

Total Benefit $1,633 $1 ,944 $311

Total Revenue 907 927 20

Consumer Surplus 726 1,017 219

Total Cost 726 1,173 266

Net Benefit 726 771 45

Producer Surplus (Profit) -0- -224 -224

Since there is no profit or loss (TG=TR), consumer surplus and net benefit

are equal

.

These results illustrate the cost recovery implication of average cost

pricing. However, as was shown, net benefit is maximized when marginal

cost pricing is used; i.e., P = MC = $33.13. The changes that occur when

price is set equal to MC are shown in the column headed P=MC. Maximizing

net benefit by using the P=MC rule increases output by 8,000 units and net

benefit by $45,000. However, this increase in net benefit entails an

operating loss ($224,355) equal to the fixed cost of the system (f + aN).

This loss will occur for e\/ery level of output and elasticity when P=MC,

F > and MC constant.

This comparison of the outcome of the decision to set P=MC with that of

setting P=AC is a specific example of the inconsistency of the goals of total

cost recovery and maximization of net social benefit with declining average

costs. The increase in total benefit ($311,000) is greater than the

29
increase in total cost ($266,000), so the choice of P=MC over P=AC can be

viewed as a socially beneficial one. However, the move to P=MC, because

of the resultant producer loss, implies a need for subsidization.

It should be noted parenthetically, that if the user market can be

segmented (e.g., students vs. professionals or daytime users vs. nighttime users), it may be possible charge different prices to each segment

and thereby use "price discrimination" to recover costs. However, with

declining average cost, price discrimination total cost recovery still

implies charging some users more than marginal cost. Thus, the use of price

discrimination in publicly funded systems raises many important questions

of equity (e.g., who pays only marginal cost). A comprehensive treatment

of the economics of price discrimination can be found in [12], especially

Chapter 5, "Decreasing Costs and Price Discrimination."

VI. REMOTE ENTRY, FIXED CAPACITY

To extend the illustration of the application of cost-benefit analysis

to the evaluation of more technologically advanced systems, a remote-entry

version of the on-site entry system will now be considered. Batch processing

rather than an interactive mode will still be assumed. While this does not

represent the most advanced technology, it permits the use or tne same queuing

model and still serves to illustrate the major points.

A. System Cost

Typically, in a remote entry system, charges are made on the basis of

the time required per search (connect time) rather than on a cost-per-search

completed basis. Because the remote entry system is subject to congestion

and increased waiting time as the utilization rate increases, user time and,

therefore, user cost increases with utilization and is not constant over
the whole range of output. Because of this, each additional user contributes

or adds to the average costs of all users, which means that the marginal cost

of the added user will be greater than the average cost.

To illustrate these points, a new set of operating procedures and

associated costs will be defined. Producer cost and user cost will be

considered separately. Next, total cost will be examined, and the impacts

of pricing alternatives on cost, cost recovery, maximization of social

benefit and the level of system utilization will be examined.

1. Producer Cost

For the remote entry example it will be assumed that access to the

system is provided through intermediaries, such as the regional medical

libraries accessing the National Library of Medicine's MEDLINE system [19],

and that requestors of searches are required to pick up the results of

their searches. Further assumptions are: no screening is performed, the

user/ system interface is provided by the intermediary users, and the service

time is the same as for the on-site entry case.

The effect of no screening is to eliminate both the fixed and the

variable screening costs, Ci* and C 8

. Requiring the user to pick-up results

eliminates both the fixed and variable mailing costs, C 5 and C 9 . Having

the intermediaries provide the user/system interface shifts the interface

cost, C 7 , to the users. Thus, for the remote entry example, total producer

costs become:

PC = f + aN = $188,525 (14)

where f = Ci + C 2 + C 3 , and the factor a and the C. are as defined for the

on-site entry example.

31
2. User Cost

For the remote entry case, the cost to users is a combination of system

charges, level of system utilization and other user incurred charges:

UC = (SC + LC) x T + FC (15)

where UC = effective cost (price) to user

SC = System charge per unit of connect time

LC = user incurred labor costs per unit of connect time

T = average connect time per search

FC = user/ system interface cost (C 7 )

The average connect time per search, T , has four components: input,

time, search time and output time as in the on-site case, plus waiting time.

Waiting time, as illustrated in Figure 3, increases as the level of

utilization, Q increases. The print-out of the search results is transmitted

directly to the remote sites but done off-line. A print-out time of 10

minutes will be assumed and added to the connect time of each search for the

example.

The system charge is assumed to include communications costs. Further,

it is assumed that the labor cost rate and interface costs are the same

among all users and constant. The labor cost rate (LC) is assumed to be

$.12 per minute for each minute of connect time.

The assumption of a constant labor cost is equivalent to assuming a

constant cost of time for users and is reasonable for the case where an

intermediary does the actual inputting. However, the shape of the cost

of time curve can play an important role in a system cost-benefit evaluation

[8, p. 889-891]. Only when all users have the same cost rate and the rate

is constant does minimizing average waiting time also serve to minimize total

user cost.

32
3. Total Cost

Total system costs are the sum of the producer cost and the user cost.

With the groundrules and assumptions described above, all producer costs

are now fixed (i.e., PMC=0). All user costs are variable and an increasing

function of utilization for any chosen system charge, SC. The curves for

SC=$50 are shown in Figure 7. The shapes of these curves do not depend on

the assumption that producer marginal cost equal zero, but only on the

assumption that the producer marginal cost be constant.

As can be seen in Figure 7, average producer cost (PAC) declines over

the whole range as in the on-site entry case. However, because the user

marginal costs (UMC) are no longer constant, the average total cost (ATC)

curve is U-shaped with UMC > ATC at all points to the right of the intersection

of the curves. This intersection occurs at about Q=32,850 and AC=MC=$34.85

for SC=$50. Raising the SC will move the UMC curve and the point of intersection upward and to the left. Thus, it is possible to manipulate the

curves to achieve a desired user marginal or average (AUC) cost at the

capacity level of output.

Since the user cost per search is dependent on the level of utilization

as well as on the system charge, it is not possible to use SC alone to

implement marginal cost pricing. Regardless of where SC is set, if price is

uniform, each user will pay the average cost. To achieve marginal cost

pricing under these conditions requires the imposition of some form of

congestion toll. The cost-benefit implication of this is examined in

the following paragraphs.

33
100 -

80

60 "

o

E

40 ~

20 -

0**30,000

TMC-UMC

10,000 20,000 30,000

Searches

40,000 50,000

Figure 7. Average, Marginal and Total Costs:

Remote Entry, Fixed Capacity

34
B. Pricing Alternatives

To illustrate the implications of pricing alternatives for the remote

entry example, assume that the convenience of the remote access system

generates a greater demand. Let there be an upward shift in the demand

curve such that the demand curve shifts from the level shown in the

on-site example with Q=28,000 when P=$33.13 to Q=28,000 when P=$40.00.

This new level of demand is shown by the demand curve D in Figure 8.

This new demand curve intersects the capacity constraint of Q*=30,000

at P=$37.70. By setting SC at $88.00, the average user cost curve (UAC)

intersects the demand curve at this same point, labeled A, in Figure 8.

Thus, if SC is set at $88.00 and average cost pricing is used, full

utilization of capacity will occur and total benefit will be maximized,

given the demand curve, D.

However, it is evident from the cost curves in Figure 8 that with

a system subject to congestion each additional user will contribute a

(marginal) cost to all users that is greater than the price paid by that

user. Thus, the additional users are imposing a higher cost on the system

than they are paying. In effect, there are cost externalities not reflected

in the (average) price.

Interestingly, under these circumstances, pricing policies designed to

injure that the unit price to users equals marginal cost will not necessarily

lead to the maximizing of net benefit. The enforcement of a policy to make

users pay marginal cost could be accomplished in the example shown in Figure 8

by adding a "congestion toll" equal to the vertical difference between UMC

and UAC at point B. This would raise the price to the user to the point

where D=MC=$41.60 and reduce the level of demand to Q=26,000.

35
10,000 20,000 30,000

Searches

40,000 50,000

Figure 8. Remote Entry Demand and Cost:

Fixed Capacity

36
Does such a quasi-marginal -cost pricing alternative result in a net

benefit greater than would result with average cost pricing? It may.

However, it may also only result in a reduction of utilization and a

higher unit price to the remaining users. This is illustrated below with

figures for the example.

Impact of changing to Marginal

Cost pricing from Average Cost

Pricing with Capacity Constraint

(Dollars in Thousands)

P=AUC

Q=30,000

P=UMC

Q=26,000

Total Benefit 2094 1934

Total Revenue 629 649

Consumer Surplus 1465 1285

Total Cost 1131 1082

User Incurred (502) (433)

System Charges (629) (649)

Net Benefit 963 852

Producer Surplus 440 460

(Dollars)

System Charge per Hour 88.00

Congestion toll

Price to User per Search 37.70

Producer Cost per Search 6.30

Producer Charge per Search 20.97 a

User Incurred Cost per Search 16.73

a) $88/hr. x 14.3 min. /search * 60 min.

b) $88/hr. x 13.8 min. /search t 60 min. + $4.75/search

88.00

4.75

41.60

7.25

24.98

1

16.92

37
The figures show that for this example, the imposition of a congestion

toll to raise user price to UMC from UAC decreases net benefit rather than

increasing it. These results illustrate two important and related

points: 1) the congestion encountered with increased utilization of a

fixed capacity remote entry system can create cost externalities,

and 2) the impact of these externalities on net benefit should be carefully

reviewed in each case since a preferred outcome is not always achieved

by making users pay marginal cost, but depends on the position and slope

of the cost and demand curves.

C. Cost Recovery

For the example chosen, cost recovery was not an issue. Even though

there was a declining producer's average cost (PAC) curve, it was below

the UAC curve over the relevant range. This is largely a reflection of the

fact that producer marginal cost (PMC) was assumed to be zero while the

UMC was assumed to be positive. If instead, PMC was positive, but also

constant, the PAC curve would shift upward while still retaining its

negative slope.

The line intersecting the capacity constraint at point C in Figure 8

shows the producer charge per search (average revenue) resulting from an SC of

$88.00. In the event that the PMC was great enough to cause the PAC curve

to shift up above this line, the question of cost recovery vs. net benefit

maximation would again occur. The same basic procedures that were applied

to the on-site entry example could be applied. The only major difference

being that the major pricing alternatives would be PAC vs. UAC rather than

PAC vs. PMC.

38
VII. CAPACITY INVESTMENT AND PRICING

In this section, the assumption of fixed capacity is relaxed, and

questions of pricing alternatives with possible changes in capacity are

examined. Capacity is not fully divisible, in the sense that additional

search capacity can be added in small increments. The relationship

between cost and capacity and assumptions as to the size-increment options

available are presented first. Next an illustration of the cost and benefit

implications of pricing and capacity investment alternatives are examined

for the on-site entry case, using the same hypothetical system cost that

was described for the fixed capacity case, modified by the amount needed

to increase capacity. Finally, these same questions are examined for the

case of remote entry, using the modified remote entry system costs.

A. System Cost and Capacity

The question of economies of scale in computing power has been given

a substantial amount of attention. As early as the 1940's H. R. Grosch

asserted that for average cost per unit of effectiveness for computer

equipment decreases substantially as the size of the computer increases.

This is a concept that has become known as Grosch* s Law [24, p. 315]. More

specifically, Grosch' s Law can be expressed as:

C/E = K/E^ (16)

where C = cost

E = effectiveness (performance or speed)

K = constant

A significant amount of empirical work has been done to examine the

validity of Grosch' s assertion [15, 16, 24, 25], Although the results

are somewhat mixed, they generally appear to support equation 16 and indicate

the existence of economies of scale in computer power.

39
For purposes of illustration and further discussion, it will be assumed

that economies exist and that they follow the pattern indicated in equation

16. However, it is important to distinguish between computing power and

computer services. Computer services can encompass a wide range of activities,

and as Selwyn [23] has demonstrated, the evidence on the existence of economics

of scale is mixed when several types of service, each with a different

production function, are offered.

Multiplying both sides of equation 16 by E gives

C = KE

h

(17)

The values for both equation 16 and equation 17 are plotted in Figure 9 as

functions of both service time and effectiveness. These were curves derived

by arbitrarily setting the effectiveness of the existing system with a

service time of 2.1166 minutes equal to one and then calculating the

effectiveness impact of decreased service time relative to that reference point.

In practice, the possible changes to system capacity are not continuous

and large indivisibilities exist. For the example, it will be assumed that

the minimum capacity increments possible, as measured in increased effectiveness or decreased service time, are fractional multiples of current

effectiveness and equal .50. Using the same criterion that W(10) > .95, new

capacity value can then be calculated for each of the service times. These

are shown in Figure 9 by the vertical lines and the corresponding Q*.

One final point is that the cost of a change in systems capacity as

contrasted to the cost of a system will entail one time conversion costs.

These costs can be significant but, tor tne example, they will not be

included. A summary of service times, computer related costs (C 3 ; and

capacity is shown below:

40
300 -

wo

co

10 1 200

W

oQ 100

4= 142,250

2.1166 1.4107 1.0583 .8466

Effectiveness

i Search Time

.7055 (Minutes)

Figure 9. Computer Cost and Copocity as a Function of Service Time

W(IO)s.95

41
Service Time

Computer Rel

Cost (C 3 )

ated Capacity: Maximum

Searches for W(10) > .95

2.1166 135,000 30,000

1.4107 165,400 56,600

1.0583 190,900 84,650

.8466 213,500 113,300

.7055 233,800 142,250

On-Site Entry

Using the capacity cost assumptions from the preceding section, it is

possible to calculate new cost curves for the on-site example. These are

shown in Figure 10. The average cost curve AC1 and the marginal cost curve

MCI are identical to those in Figure 6. The curves AC2 and MC2 are the

corresponding curves for the capacity investment which increases effectiveness

50%, reducing service time to 1.4107 minutes and increasing capacity to

56,600 searches per year.

Assume again a one time shift in demand from the level shown in

Figure 6, this time to the level shown by the curve D in Figure 10- This

D curve intersects the MCI in the vertical section at Q=30,000 and P=$50.00.

The curve also intersects the AC2 curve at Q=37,900 and P=$39.90 and the MC2

curve at Q=45,740 and P=$33.13.

The alternatives open to the producer are to ration existing capacity

by charging $50.00 per search (alternative 1); to expand capacity and price

at average cost of $39.90 (alternative 2); or to expand capacity and set

P=MC2 (alternative 3). The outcomes for each of these decisions are

tabulated below:

42
90 -

" ACI

D

MC 1 MC2

70 \aC2

Dollars

en O

-

AC2

30 ^—

D

10 -

1 1 1 1 «

1 1 1 1 1 1 1 10 20 30

Searches (Thousands)

40 50

Figure 10. Pricing and Capacity Alternatives;

On-Site Entry

43
Impact of Alternative

Pricing and Capacity Decisions

Alt. 1 Alt. 2 Alt. 3

values at values at values at

Q=30,000 Q=37,900 Q=45,740

and P=MCI and P=AC2 and P=MC2

Total Benefit 2700 3056 3345

Total Revenue 1500 1512 1515

Consumer Surplus 1200 1544 1830

Total Cost 1249 1512 1789

Net Benefit 1451 1544 1556

Producer Surplus 251 -- - 274

These figures show that the first alternative involves a significant

producer surplus. Moving to the second alternative results in an increase

in net benefit but entails the elimination of the producer surplus. The

third alternative further increases net benefit but again entails a producer

loss equal to the fixed cost of production. As with the fixed capacity

case, the alternative which maximizes net benefit (alternative 3) significantly

increases output and lowers price but entails a loss to the extent of fixed

cost. Thus, the example illustrates that for systems with constant marginal

cost, with or without fixed capacity, strategies which increase utilization

can lead to higher net benefit while implying producer loss.

C. Remote Entry

Since capacity investment for the remote entry system reduces service

time, it also reduces waiting time and, therefore, cost to users for any

given level of utilization. Thus, such a producer investment has a direct

impact on user costs in addition to its effect on total net benefit. The

impacts of pricing alternatives with a change in capacity will be illustrated

using the same demand curve that was used for the remote entry, fixed capacity

example. This curve is shown in Figure 11 as the curve labeled D.

44
10,000 20,000 30,000

Searches

40,000 50,000 60,000

Figure il. Pricing and Capacity Alternatives:

Remote Entry

45
The point A in Figure 11 is the point where UAC=D for the old service

time of two minutes and a system charge of $88.00. The curve PAC is the

producer's average cost curve for that same service time. The curve UAC

is the user average cost curve resulting from reducing service time to

1.4107 minutes (increasing capacity to 56,600) with the same service

charge of $88.00. As can be seen this curve now intersects the demand

curve at about Q=35,000 and P=$32.00, illustrating how capacity investments

shift the UAC curves downward and to the right.

Using the point A and Q*=30,000 as a point of departure, the major

alternatives which will be compared are: continue with the existing

practice (i.e., point A), increase capacity and set price to maximize net

benefit, and increase capacity and set price to recover cost. The results

of the first alternative were calculated for the fixed capacity example,

and are summarized again in the first column headed "Point A" in Table 1.

To achieve the second alternative, it is first necessary to increase

the capacity cost. Again a capacity investment which increases effectiveness

by 50 per cent and capacity to 56,600 searches by reducing service time to 1.4107

minutes will be used for the example. This shifts producer's average cost

up. This is illustrated in Figure 11 by the curves PAC which corresponds

to Q*=30,000 and PAC1 which corresponds to Q*=56,600.

With the appropriate reduction in SC, it is possible to again maximize

total benefit by having P=UAC1=D at Q*=56,600. For the example this occurs

when SC=$3.55. The resulting UAC1 at Q*=56,600 is $17.50. A summary of

the impacts of increasing capacity and pricing to maximize total benefit

is shown in the second column headed P=UAC1 in Table 1.

46
TABLE 1

IMPACT OF ALTERNATIVE PRICING DECISIONS WITH

EXPANDED CAPACITY FOR THE REMOTE ENTRY EXAMPLE

(Dollars in Thousands)

Total Benefit

Total Revenue

Consumer Surplus

Total Cost

User Incurred

System Charges

Net Benefit

Producer Surplus

(Dollars)

System Charges per Hour

Surcharge

Price to User per Search

Producer Cost per Search

Producer Charge per Search

User Incurred Cost per Search

POINT A

Q=30,000

2094

629

1465

1131

(502)

(629)

963

440

88.00

37.70

6.30

20.97a

16.73

P=UAC1

Q=56,600

P=TAC1

Q=49,500

2800 2661

48 219

2752 2442

1209 1042

(738)

(471)

(823)

(219)

1591 1619

-171 -0-

3.55 3.55

- 3.64

17.50 20.90

3.85

.85

b

4.42

.78

c

16.65 16.47

a) $88.00/hr. x 14.3 min. /search * 60 min.

b) $3.55/hr. x 13.9 min. /search t 60 min.

c) $3.55/hr. x 13.2 min. /search j, 60 min.

47
The increase in the net benefit between this alternative and the

"Point A" alternative is quite significant. However, in this example,

unlike the fixed capacity case, maximizing total benefit implies a producer

loss. The average producer income per search resulting from setting

SC=$3.55 is $.85 at Q*=56,600. This is shown by the horizontal line

which intersects the capacity constraint at the point labeled C. The

average producer cost at this point is $3.85 as shown by the intersection

of the curve PAC1 and the capacity constraint.

A cost recovery strategy for this example would be to add a surcharge

to UAC1 sufficient to cover the producer cost. This will occur when

P=TAC1=D, where TAC1=UAC1+PAC1 . To illustrate this the total cost curve

TAC1 is also shown in Figure 11. This TAC1 curve intersects the demand

curve at point B for Q=49,500. At this Q, PAC1 is $3.64, which is the

vertical distance from point B to the UAC1 curve at Q=49,500. Thus,

adding a surcharge of $3.64 per search would result in a demand level

of Q=49,500 at a user price per search of $20.90. The results of this

alternative are shown in column three of Table 1 headed P=TAC1 . As

expected, the cost recovery strategy again produces a slight increase

in net benefit compared to P=UAC1 decision.

However, the most significant point is that as capacity increases

relative to demand, the influence of waiting time is reduced and average

and marginal cost become almost constant. (In the example, p=.85 at

Q=50,000 for Q*=30,000,as compared to p=.57 at Q=50,000 for Q*=56,600.)

As a result, for high relative capacity, the remote entry system cost

curves become increasingly like the on-site system cost curves with

declining average (producer) cost and constant marginal (producer and

user) cost.

48
VIII. POLICY IMPLICATIONS

The examples presented illustrate the various ways in which declining

average cost occurs in the operation of automated scientific information

retrieval systems, and indicate the way in which conflicts can arise between

cost recovery and the maximization of net social benefit. Declining

average costs, and "public good" properties can be taken as justification

for public subsidy. Having demonstrated the existence of declining average

costs for at least some instances for automated scientific information

retrieval systems, the questions then become: what are public goods, and

can automated scientific information retrieval systems be viewed as public

goods?

A. Public Goods

The features of a public good or service which distinguish it from

other goods and services produced in the economy have been examined

extentively [7, 9, 20, 27] and can be characterized as follows:

"There are certain goods that have the peculiarity that

once they are available no one can be precluded from

enjoying them whether he contributed to their provision

or not. These are the public goods. Law and order is

an example, and there are many others too familiar to

make further exemplification worthwhile. Their essential

characteristic is that they are enjoyed but not consumed

(and that their benefits are derived) without any act

of appropriation" [7, p. 4].

49

.,-,— _..-,.»-—....—

,

m
Two important features of public goods are: since no one can be

precluded from enjoying their benefits, the price mechanism is ineffective

as a means for allocating the enjoyment of their benefits; and since they

are "enjoyed but not consumed" the costs of providing these goods is

largely unaffected by the number of persons benefiting from them. Because

of these implications, public goods are generally provided by government

or by publicly financed organizations.

B. Semi -Public Goods

Some goods or services, though not pure public goods have some attributes

of public goods combined with some attributes of private goods. Returning

to the notation of equation 10, a formal definition of such a "semi -public"

good is the following: Let

TC = F + bQ

where F is the fixed component, b is the cost per unit of output per unit

of time, and Q is the number of units of output per unit of time. Then,

"If we 'all enjoy in common' a collective good, the case

where b=0 characterizes a pure collective good, since no

additional cost is necessary for an additional consumer

to enjoy it. If F=0 we are at the other extreme where

there is no element of communal ity. We occupy the

in-between situation of semi-public good if F > 0,

constituting the common component of the good, and b > o,

constituting its private component." [1, p. 666]

Thus if the good or service is in some sense a "collective good" (i.e.,

a public good), subsidization, at least up to the value of F should be

given consideration if declining average costs are also present.

50
C. Automated Information Systems

Using a logic similar to that set forth for journal publications [l

,

p. 665-666], it would appear that automated information retrieval systems

do indeed have public good as well as private good attributes and can be

viewed as semi-public goods. The publications indexed and abstracted in

the data base and representing the ideas contained in the publications are

the core of the public good component of automated information retrieval

systems. This information is not consumed when it is used, and in that

sense availability to some does not reduce availability to others. In

addition, the cost of the original research, editing and printing may

be borne by scholars, universities, foundations and other parts of the

public sector.

However, the benefits of automated information systems cannot be

simply enjoyed without special provision for access to the ideas contained.

This access is consumed and affects the availability of the information

retrieval service to others when it is consumed. Thus, automated information

retrieval systems have a private good aspects as well as a public good

aspect and, in this sense, are a semi-public good.

The conclusion that automated scientific information retrieval systems

do have public goods attributes and, in some cases, declining average costs

leads to the following major conclusion regarding the subsidization of these

systems. If it can be demonstrated that declining average costs persist

for all reasonable pricing and capacity alternatives, a given information

retrieval system should be subsidized up to the difference between producer

average total cost and producer marginal cost. A corollary conclusion is

that the subsidization of each system should be periodically reviewed to

determine if the initiating conditions for subsidization continue to exist.

51
APPENDIX A

MAXIMIZATION OF NET SOCIAL BENEFIT

Net benefit, NB, can be expressed as:

NB = TB - TC, (A-l)

where,

TB = Total Benefit = TR + CS

TC = Total Cost

TR = Total Revenue

CS = Consumer Surplus

Differentiating Equation A-l with respect to output and setting the result

equal to zero, it is possible to solve for the net-benefit-maximizing or

optimal price:

^ = 3Jf(TR + CS) v^-O. (A-2)

Since (TR + CS) =/*q P(Q)dQ, where

J a P(Q) is the demand curve [28, p. 812], the term 4r (TR + CS) = price, P.

By definition, marginal cost, MC, is the cost of producing the last unit

d

of output so that MC e jq (TC). Thus, Equation A-2 shows that total net

benefit is maximized when P = MC. The demand curve is also the average

revenue curve since TR = Q x P; therefore, P = MC = AR when net social benefit

is maximized, and P is the point of intersection of MC and the demand curve

(see point B in Figure 2).

With a fixed capacity, the problem of optimal pricing becomes one of

constrained maximization; i.e.,

max. NB = (TR + CS) - TC

(A-3)

for Q < Q* ,

52
where Q* is the maximum attainable output level. The solution of this problem

requires the use of a Lagrangian multiplier, denoted as X [28, p. 812]. Using

a Lagrangian, equation A-3 becomes:

max. L(q,X) = (TR + CS) - TC - X(Q-Q*). (A-4)

Differentiating partially with respect to Q and X, and equating the results

to zero gives the benefit maximizing solution:

P = MC + X. (A-5)

If the constraint is not operative (i.e., Q < Q*), then X = and the optimal

price is P = MC [28, p. 813].

53
REFERENCES

1. Barzel , Y., "The Market for a Semipublic Good: The Case of the American

Economic Review," The American Economic Review , September 1972,

pp. 665-674.

2. Berg, S. V., "An Economic Analysis of the Demand for Scientific Journals,"

Journal of the American Society for Information Science , Jan-Feb 1972,

pp. 23-29. "

"

3. Bryant, E. C. and D. W. King, The Evaluation of Information Services

and Products , Information Resources Press, Washington, D.C., 1971.

4. Cuadra, C, ed., Annual Review of Information Science and Technology , Chapter entitled "Design and Evaluation of Information Systems," • by D. W. King (Vol. 3, 1968), M. M. Henderson (Vol. 4, 1969), F. W. Lancaster and C. T. Gillespie (Vol. 5, 1970), C. W. Cleverdon

(Vol. 6, 1971), and "Costs, Budgeting and Economics of Information

Processing," by J: H. Wilson, Jr., (Vol. 7, 1972), American Society

for Information Science, Washington, D.C.

5. Danilov, V. J., C. Herring and D. J. Hillman, Report of the Panel on Economics of the Science Information Council , Office of Science

Information Services, National Science Foundation, January 1973.

6. Dei Rossi, J. A. and G. Mills, "A Telephone Access Biomedical Information

Center, Operations Research , Vol. 20, No. 3, May-June 1972, pp. 643-667,

7. Dorfman, Robert, "General Equilibrium with Public Goods," presented to

International Economics Association Conference on Public Economics,

September, 1966.

8. Greenberger, M. , "The Priority Problem and Computer Time Sharing,"

Management Science , Vol. 12, No. 11, July 1966, pp. 888-906.

9. Herring, C, et. al . Report of the Task Group on the Economics of Primary

Publication , Committee on Scientific and Technical Communications,

National Academy of Sciences, Washington, D.C, 1970.

10. Ireson, W. G. and E. L. Grant, ed., Handbook of Industrial Engineering , Prentice Hall, New Jersey, 1957

11. International Business Machines, Analysis of Some Queuing Models in

Real Time Systems , IBM Data Processing Techniques Manual F20-0007-1

,

White Plains, New York.

12. Kahn, A. E., The Economics of Regulation, Vol. I, Economic Principles , John Wiley & Sons, Inc., 1970. - ~

...

13. Kantor, H., A. Moore and N. Singer, "Prices and the Allocation of Computer

Time," Proceedings of the Fall Joint Computer Conference , 1968 , pp. 493-498.

54
14. King, D. W. , Cost/Benefits Analysis , Westate Research, Inc., Bethesda, Md.,

1969.

15. Knight, K. E., "Evolving Computer Performance," Datamation , January 1968.

16. Knight, K. E., "Changes in Computer Performance," Datamation , September

1966, pp. 40-54.

17. Krutilla, John V., "Efficiency Goals, Market Failure and the Substitution

of Public for Private Action," The Analysis and Evaluation of Public

Expenditures : The PPB System , A Compendium of Papers submitted to the

Subcommittee on Economy in Government of the Joint Economic Committee,

Congress of the United States, Vol. 1, U.S. Government Printing Office,

Washington, D.C., 1969, pp. 277-289.

18. Lancaster, F. W. , "The Cost-Effectiveness Analysis of Information Retrieval

Systems," Journal of the American Society for Information Science , January-February 1971, pp. 12-27.

19. McCarn, D." B. and J. Leiter, "On-Line Services in Medicine and Beyond,"

Science , Vol. 181, July 27, 1973, pp. 318-324.

20. Milliman, J. W., "Beneficiary Charges and Efficient Public Expenditure

Decisions," The Analysis and Evaluation of Public Expenditures : The

PPB System , A Compendium of Papers submitted to the Subcommittee on Economy in Government of the Joint Economic Committee, Congress of

the United States, Vol. 1, U.S. Government Printing Office, Washington,

D.C., 1969, pp. 291-318.

21. Morse, P. M. , Library Effectiveness : A Systems Approach , The M.I.T.

Press, Cambridge, Massachusetts, 1969.

22. Park, M. J., J. L. Carmon and R. E. Stearns, "The Development of a General Model for Estimating Computer Search Time for CA Condensates,"

Journal of Chemical Documentation , Vol. 10, No. 4, 1970, pp. 282-284.

23. Selwyn, L. L., "Competition and Structure in the Computer Service

Industry," Economic Considerations in Managing the Computer

Installation , Proceedings of the Second Annual SIGCOSIM Symposium,

October 26, 1971, Burton E. Squires, Ed., Association for Computing

Machinery, New York, 1971.

24. Sharpe, W. F., The Economics of Computers , R-463-PR, The Rand Corporation,

Santa Monica, California, August 1969.

25. Solomon, M. B., Jr., "Economies of Scale and the IBM System/360,"

Communications of the ACM , Vol. 9, No. 6, June 1966, pp. 435-440.

26. Syski, R., Introduction to Congestion Theory In Telephone Systems , Oliver

and Boyd, London, 1960.

55
27. Vickery, W. S., "Decreasing Costs, Publically Administered Prices and

Economic Efficiency," The Analysis and Evaluation of Public

Expenditures : The PPB System , A Compendium of Papers submitted to

the Subcommittee on Economy in Government of the Joint Economic

Committee, Congress of the United States, Vol. 1, U.S. Government

Printing Office, Washington, D.C., 1969, pp. 119-148.

28. Williamson, 0. E., "Peak-Load Pricing and Optimal Capacity," The

American Economic Review , Vol. 56, No. 4, September 1966, pp. 810-827,

56
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS Technical Note 8642. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Cost Recovery in Pricing and Capacity Decisions

for Automated Information Systems

5. Publication Date April 1975

6. Performing Organization Code

7. AUTHOR(S)

James A. Dei Rossi

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 640.1404

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Office of Science Information Services

National Science Foundation

Washington, D. C. 20550

13. Type of Report & Period Covered Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 75-600015

16. ABSTRACT (A 200-word or less tactual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

This paper examines the cost- benefit implications of alternative pricing and capacity

investment decisions for automated scientific and technical information retrieval

systems. Two typical systems are examined and numerical examples presented.

In the first system, search requests are entered on-site. The numerical examples

show how setting price to maximize net social benefit precludes total cost recovery

and implies subsidization. In the second hypothetical system, search requests are

entered from remote access terminals. Allowance is made for random arrival rates,

and distinction is made between system charges to users and other user incurred cost

With these refinements, the numerical examples show how, for certain ranges of output, total cost recovery is consistent with the maximization of net social benefit. The

paper then examines the "public good" attributes of scientific and technical informatio

retrieval systems and concludes that such systems can be viewed as "semi- public

goods," since the information stored has the characteristics of a public good while access to this information has the characteristic of a private good. Based on the

public good considerations and the numerical examples, the paper concludes that

subsidization for the fixed costs is warranted to the extent that all reasonable

alternatives which maximize net social benefit preclude total cost recovery.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Automated information retrieval; cost benefit; public good; scientific and technical

information; semi -public good; subsidization; total cost recovery; user charges

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